# What is the adjusted Rand index?

### Sommario

- What is the adjusted Rand index?
- What is Rand index in clustering?
- What does a negative adjusted Rand index mean?
- Is Rand index accurate?
- How do you read the Rand index?
- What is Davies Bouldin score?
- How do you interpret the adjusted Rand index?
- What is V measure?
- What is Agglomerativeclustering?
- How is Davies-Bouldin index calculated?

### What is the adjusted Rand index?

The adjusted Rand index is **the corrected-for-chance version of the Rand index**. Such a correction for chance establishes a baseline by using the expected similarity of all pair-wise comparisons between clusterings specified by a random model.

### What is Rand index in clustering?

The Rand Index **computes a similarity measure between two clusterings by considering all pairs of samples and counting pairs** that are assigned in the same or different clusters in the predicted and true clusterings.

### What does a negative adjusted Rand index mean?

Negative ARI says that **the agreement is less than what is expected from a random result**. This means the results are 'orthogonal' or 'complementary' to some extend.

### Is Rand index accurate?

Rand index is **accuracy computed not in the raw data** (which does not work unless you have you data where class 1 is cluster 1). Instead, it is the accuracy on pairs of points, which is invariant to renaming clusters.

### How do you read the Rand index?

The Rand index may be interpreted as **the ratio of the number of object pairs placed together in a cluster in each of the two partitions** and the number of object pairs assigned to different clusters in both partitions, relative to the total number of object pairs.

### What is Davies Bouldin score?

Compute the Davies-Bouldin score. The score is defined as **the average similarity measure of each cluster with its most similar cluster**, where similarity is the ratio of within-cluster distances to between-cluster distances. Thus, clusters which are farther apart and less dispersed will result in a better score.

### How do you interpret the adjusted Rand index?

Details. The adjusted Rand Index (ARI) should be interpreted as follows: ARI >= 0.90 excellent recovery; 0.80 =< ARI < 0.90 good recovery; 0.65 =< ARI < 0.80 moderate recovery; ARI < 0.65 poor recovery.

### What is V measure?

The V-measure is **the harmonic mean between homogeneity and completeness:** **v = (1 + beta) * homogeneity * completeness** / (beta * homogeneity + completeness) This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won't change the score value in any way.

### What is Agglomerativeclustering?

The agglomerative clustering is **the most common type of hierarchical clustering used to group objects in clusters based on their similarity**. It's also known as AGNES (Agglomerative Nesting). ... Next, pairs of clusters are successively merged until all clusters have been merged into one big cluster containing all objects.

### How is Davies-Bouldin index calculated?

For each cluster, its nearest neighboring cluster is identified, and **the sum of their intracluster variances is divided by the difference between their centroids**. This value is calculated for each cluster, and the Davies-Bouldin index is the mean of these values.